Philosophy 103
Linguistics 103
Yet, still, Even further More and yet
more
Introductory Logic:
Critical Thinking
Dr. Robert Barnard
Last Time:
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Introduction to Categorical Logic
Aristotle’s Categories
Leibniz, Concepts, and Identity
Analytic – Synthetic Distinction
Essence and Accident
Necessary and Sufficient Conditions
Plan for Today
• Categorical Propositions
– Parts and Characteristics
– Conditional and Conjunctive Equivalents
– Existential Import
Reminder !!!!!
Thursday, September 13, 2007
4:00 PM
Bryant 209
Philosophy Forum Talk –
“Einstein on the Role of History and Philosophy of
Science in Physics”
Dr. Don Howard – University of Notre Dame
Extra Credit: 1 page reaction, due in 2 weeks (9/27)
Categorical Propositions
Categorical Propositions relate one category (in
whole or part) as indicated by the SUBJECT
TERM to another category, indicated by the
PREDICATE TERM (either affirmatively or
negatively):
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All houses have roofs
Some buildings are houses
No eggs are shatterproof
Some people are not paying attention
UNIVERSAL CATEGORICAL
PROPOSITIONS
A Categorical Proposition that makes a claim
about the entire SUBJECT CLASS is called a
UNIVERSAL CATEGORICAL PROPOSITION
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All Toys…
No Fish…
All Bugs…
No people from Georgia…
PARTICULAR CATEGORICAL
PROPOSITIONS
A Categorical Proposition that makes a claim
about one or more members of the SUBJECT
CLASS is called a PARTICULAR CATEGORICAL
PROPOSITION
• Some Eggs…
• Some men…
• Some Lithuanians…
QUANTITY
All categorical propositions are either:
UNIVERSAL or PARTICULAR
We call this the QUANTITY of the
proposition.
AFFIRMATIVE AND NEGATIVE
PROPOSITIONS
When a categorical proposition asserts the
existence of a relationship between the
Subject term and the Predicate term we say
that the proposition is AFFIRMATIVE.
When a categorical proposition denies the
relationship between the Subject term and
the Predicate term we say that the proposition
is NEGATIVE
QUALITY
All categorical propositions are either:
AFFIRMATIVE or NEGATIVE
We call this the QUALITY of the
proposition.
THE 4 TYPES of CATEGORICAL
PROPOSITION
UNIVERSAL
PARTICULAR
AFFIRMATIVE
ALL S is P
SOME S is P
NEGATIVE
NO S is P
SOME S is not P
Questions?
THE UNIVERSAL AFFIRMATIVE
ALL S is P
TYPE A
If (x is S) then (x is P)
Conceptual Claim
THE UNIVERSAL NEGATIVE
No S is P
TYPE E
If (x is S) then (x is not P)
Conceptual Claim
PROPOSITIONS ABOUT INDIVIDUALS
In CATEGORICAL LOGIC a proper name denotes a class with
one member.
• Socrates: the class containing Socrates
• Al Gore: the class of Al Gore
• Brad Pitt: The class containing Brad Pitt
• …etc…
SO, a proposition like ‘Socrates is a man’ is really about the
whole class Socrates, so…
It is a UNIVERSAL proposition!!!
Universal Propositions
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2.
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6.
7.
All Dogs are Brown
All Houses are residences
No Pigs have wings
No Cars are Airships
No Humans have quills
All Wisdom is not Folly
John Jay was the first Chief Justice
THE PARTICULAR AFFIRMATIVE
Some S is P
TYPE I
At least one thing X is Both S and P
For at least one x (x is S) and (x is P)
Existential Claim
THE PARTICULAR NEGATIVE
Some S is not P
TYPE O
At least one thing X is S and not P
For at least one x (x is S) and (x is not P)
Existential Claim
Particular Propositions
1.
2.
3.
4.
5.
6.
Some Cats are red.
Some Pigs are not Sows
Some lettuce is not endive.
Some Men are not Women
Some Flowers are plants.
Some Presidents of the United States served
two terms
7. Some Ole Miss coaches used to win games.
EXISTENTIAL IMPORT
ONLY a proposition with EXISTENTIAL IMPORT
requires that there be an instance of the
SUBJECT TERM in reality for the proposition to
be true.
• All Dogs have 4 Legs (Conceptual – no EI)
• Some Fish are Red (Existential – EI)
QUANTIFIER AND QUALIFIER
The Term which determines the QUANTITY of
the proposition is called THE QUANTIFIER
ALL – NO -- SOME
The term that determines the QUALITY of the
proposition is called the QUALIFIER
ALL – NO – IS – IS NOT
A, E, I, and O
TERM
Proposition Form
Quantity
Quality
A
ALL S IS P
UNIVERSAL
AFFIRMATIVE
E
NO S IS P
UNIVERSAL
NEGATIVE
I
SOME S IS P
PARTICULAR
AFFIRMATIVE
O
SOME S IS NOT P
PARTICULAR
NEGATIVE
COPULATION!!!!
Every Categorical Proposition has a Quantity and
Quality, a Subject term and a Predicate Term. There
is one more part:
THE COPULA
All S is P
No S is P
Some S is P
Some S is not P
Questions?
Questions?
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Categorical Propositions
Conditional and Conjunctive equivalents
Existential Import
Traditional Square of Opposition
Modern Square of Opposition
Existential Fallacy
Venn Diagrams for Propositions
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Immediate Inferences
Conversion
Contraposition
Obversion
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Syllogistic Logic
Form- Mood- Figure
Medieval Logic
Venn Diagrams for Syllogisms (Modern)
Week • Venn Diagrams for Syllogisms (traditional)
• Limits of Syllogistic Logic
• Review of Counter-Example Method
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Logic of Propositions
Decision Problem for Propositional Logic
Symbolization and Definition
Translation Basics
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Truth Tables for Propositions
Tautology
Contingency
Self-Contradiction
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Truth Tables for Propositions II
Consistency
Inconsistency
Equivalence
Week • Truth Table for Arguments
• Validity / Invalidity
• Soundness
Week • Indirect Truth Tables
• Formal Construction of Counter-Examples
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Logical Truths
Necessity
Possibility
Impossibility